Removing alpha from PNG image with set alpha node gives pixelated result
Sometimes in PNGs that have alpha channel the image get interpreted in a weird way as RGB only (without the alpha).
Here's an example of how blender interprets such image:



Maybe someone else can explain why... I find that the program in which PNGs are generated can make a difference.

But as a quick solution in this particular case, try connecting the alpha of your Image node to the alpha of the Set Alpha node.